Symbol estimation using soft-output algorithm and feedback

ABSTRACT

In a mobile communication system, a method and circuit for symbol estimation is described. According to the method, a soft output decision for a symbol is estimated and is fed back to modify decisions made for a subsequent set of received samples. This has the advantage of conveying not only information about the most likely symbol, but also information about the noise environment.

FIELD OF THE INVENTION

[0001] The present invention relates to symbol estimation in a mobilecommunication system.

BACKGROUND

[0002] In high data rate mobile communication, system performance isdegraded heavily by intersymbol interference ISI. The equalisationtechnique is one of the main issues for a receiver to combat ISI. It iswell established that maximum likelihood sequence estimation MLSE,implemented by the Viterbi algorithm can provide optimum performance interms of sequential error event probability. This technique however hasgreat computational complexity which hinders it from use for channelswith a long delay spread. In particular, when the technique isimplemented using a trellis structure, the complexity of the trellisstructure increases exponentially with channel length. Channel length isa time period which is defined as the influence depth (time duration) ofeach symbol. With a symbol transmitted at time t₀, the symbol will beheard most significantly between times t₁ to t₂ (subsequent to t₀). Thechannel length is considered to be t₂−t₁.

[0003] It is an aim of the present invention to reduce the complexity ofsymbol estimation, particularly but not exclusively for implementingsymbol estimation in channels with a long delay spread using a trellisstructure.

SUMMARY OF THE INVENTION

[0004] According to one aspect of the present invention there isprovided a method of estimating symbols transmitted between a mobilestation and a base station in a communication system comprising:

[0005] receiving via a communication channel a set of received signalsamples which have travelled via different transmission paths, eachsignal sample conveying a symbol component;

[0006] estimating from the set of received signal samples a soft-outputdecision for the symbol which combines over a number of symbolcomponents an estimated value for each symbol component with alikelihood parameter which indicates a level of reliability associatedwith that estimated value; and

[0007] using the soft-output decision as a feedback element to modify asubsequent set of received signal samples prior to estimating a softoutput decision for the subsequent set of received samples.

[0008] According to another aspect of the present invention there isprovided a symbol estimation circuit for use in a mobile communicationsystem for estimating symbols, the circuit comprising:

[0009] a receiver arranged to receive via a communication channel a setof signal samples which have travelled via different transmission paths,each signal sample conveying a symbol component;

[0010] a estimator for estimating from the set of received signalsamples a softoutput decision for the symbol which combines over anumber of symbol components an estimated value for each symbol componentwith a likelihood parameter which indicates a level of reliabilityassociated with that estimated value; and

[0011] a feedback path for feeding back the soft-output decision tomodify a subsequent set of received signal samples prior to estimating asoftoutput decision for the subsequent set of received samples.

[0012] The symbol estimation technique can be used recursively eitherwithin signal bursts or between signal bursts. That is, in acommunication system wherein a sequence of signal bursts are received bythe communication channel, a soft-output decision for each symbol in thesignal burst may be estimated and used as a feedback element prior toestimation of a subsequent symbol in the same signal burst.Alternatively, a soft-output decision for a preceding signal burst canbe used for a subsequent signal burst. The former is more likely to bereliable.

[0013] Estimation of the soft-output decision for the symbol can becarried out in a trellis equaliser in which state transitions areeffected via a set of transition branches. The states for the trellisequaliser can initially be defined by channel taps of a channel impulseresponse estimated from the receive signal samples.

[0014] In the described embodiment, a first set of the channel taps isutilised for setting the initial states in a trellis equaliser and asecond set of the channel taps are treated as interference and used tomodify the input signal prior to estimating a subsequent soft-outputdecision.

[0015] A minimum phase channel impulse response can be generated usingan all path prefilter.

[0016] In the technique according to the following described embodimentsof the invention, a suboptimum softoutput algorithm SSA is used as afeedback decision as a tradeoff between optimality and implementationreality. The algorithm can be implemented using a trellis structure. Thecomputational power needed for the described suboptimum softoutputalgorithm is in the same range as that of using a Viterbi algorithm, butthe memory needed is much less. Moreover, the algorithm generates asoft-output decision rather than a hard decision and the inventors havenoted that soft decision feedback can give better performance than harddecision feedback for a low signal to noise ratio domain.

[0017] For a better understanding of the present invention and to showhow the same may be carried into effect reference will now be made byway of example to the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

[0018]FIG. 1 is a block diagram illustrating schematically symbolestimation in accordance with one embodiment of the invention;

[0019]FIG. 2 is an equivalent discrete time model of a channel withassumed intersymbol interference ISI and additive white Gaussian noise(AWGN);

[0020]FIG. 3 is an equivalent model illustrating the principle ofdecision feedback with split channel taps;

[0021]FIG. 4 is a graph showing simulation results comparing no decisionfeedback with hard decision feedback and soft decision feedback withouta prefilter;

[0022]FIG. 5 is a graph showing simulation results as for FIG. 4 butwith a prefilter; and

[0023]FIG. 6 is simulation results showing a comparison of feedbackusing full channel taps and split channel taps.

DESCRIPTION OF THE PREFERRED EMBODIMENT

[0024]FIG. 1 denotes schematically the principles of the invention. Thecomponents of FIG. 1 may form part of receiving circuitry either withina mobile phone or within a base station. An incoming signal z issupplied to a channel impulse response block 1 which generates a channelimpulse response in the form of a plurality of channel taps h_(O) . . .h_(L) in a manner which is known and which will not be described furtherherein. For the purposes of the present embodiment, the channel impulseresponse can be considered to be held in two stores which are denoted 3and 5. Of course, these could form part of a common memory. The firststore 3 holds a first part of the channel impulse response in the formof channel taps h_(O) . . . h_(L1) and the second store 5 holds a secondpart of the channel impulse response in the form of channel tapsh_(L1+1) . . . h_(L). The channel taps are supplied to a channelestimator which estimates for each received signal sample z_(K) a firstset of estimated channel taps h_(O) . . . h_(L1) and a second set ofestimated channel taps h_(L1+1) . . . h_(L). It will be appreciated thatthe channel impulse response taps themselves are generated using asequence of received signal samples over a period of time, for examplethe training sequence. The channel estimator generates estimated channeltaps appropriate for the received signal sample z_(k) at time k.

[0025] The first set of estimated channel taps h_(O) . . . h_(L1) aresupplied to a trellis equaliser 9 which has M_(L1) states defined by theestimated channel taps. The operation of the trellis equaliser isdescribed in more detail in the following. The second part of theestimated channel taps h_(L1+1) . . . h_(L) are supplied to aninterference remover ilithe function of which will shortly be described.

[0026] The trellis equaliser 9 generates an estimate for the transmittedsignal element Uk corresponding to the received signal sample z_(k).This is referred to herein as a softoutput decision. Within the trellisequaliser this has been done by combining a number M of symbolcomponents A together with a likelihood for each component to generatean estimate ak of the transmitted symbol. This is described in moredetail in the following.

[0027] The soft-output decision for the transmitted signal element u_(k)is fed back to the input of the trellis equaliser 9 to modify subsequentdecisions generated by the trellis equaliser. In the circuitryillustrated in FIG. 1, “interference” based on the second part of theestimated channel taps is first removed by the interference remover 11.Then, at the subtracter 13 an interfering signal based on a calculationutilising the soft-output decision and the estimated channel taps of thesecond part are subtracted from subsequent incoming samples z_(k). Theinterference remover 11 performs the following function:

[0028] ${\sum\limits_{j = {{L1} + 1}}^{L}u_{k}} -_{j}h_{j}$

[0029] The estimated transmitted signal elements u_(k) are supplied to adecoder, such as a Viterbi decoder for providing decoded bitsrepresenting the message conveyed by the signal.

[0030] An all path prefilter 17 placed after the channel estimator 7 canensure a minimum phase channel impulse response.

[0031] The theory underlying the present invention will now bediscussed. A communication channel can be described as a finite statemachine as represented in FIG. 2. In FIG. 2, blocks denoted Z⁻¹represent successive path delays and the block denoted 2 represents asumming function. Using Forney's whitened matched filter as described inG. D. Forney, “Maximum likelihood sequence estimation of digitalsequences in the presence of intersymbol interference”, IEEE Transactionon Information Theory, Vol. IT-18, pp. 363-378, 1972, the channel can berepresented by a discrete-time equivalent low-pass model, comprisingintersymbol interference (ISI) and additive white (memoryless)stationary noise n_(k) with probability density function (pdf)p_(n)(n_(k)) Thus, a received signal sample z_(k) at time k comprises atransmitted signal element u_(k) and a noise element n_(k). The channelimpulse response h, assumed to be available before the symbolestimation, is denoted by a plurality of channel taps h_(O) . . . h_(L)as in equation (1) where L denotes the channel length.

[0032] For the additive white Gaussian noise n_(k) (AWGN), theprobability density function (pdf) p(n_(k)) is given by Equation (2)where σ² is the variance of the noise.

[0033] The complex-valued transmitted symbols a_(k) are denoted byEquation (3) where M denotes the size of the signal set, i.e. the numberof symbol components A which are summed to generate a transmitted symbola_(k).

[0034] The discrete-time channel model can be described by a trellisdiagram with Z=M^(L-1) states, where each state S_(k) is defined byEquation (4).

[0035] The received signal at time k, z_(k), is compared with each of aset of assumed signal elements

(ξ_(k)) (the reference values) to form the so-called Euclidean distanced(ξ_(k)) as defined in Equation (5) where ξ_(k) are the transitionbranches from one of the valid predecessor states, S_(k-1). Obviously,at each time, there are M transition branches from and to each state.

[0036] In the following described embodiment:

[0037] The trellis equaliser is implemented in hardware using ashift-register for holding the states S_(k). Initial states of theshift-register are known beforehand.

[0038] Channel taps are available for the sequential estimation.

Derivation of Soft-output Algorithm

[0039] According to Bayes theorem, the probability p that the receivedsamples from time index 1 to k z₁ ^(k) represent a transmitted signalelement subject to a fixed decision delay D, U_(k-D), is given byEquation (6).

[0040] The second probability in (6) which corresponds to the forwardrecursion can be calculated as in Equation (7) where Q is the set of Mstates of S_(k), which lead to the state S_(k+1). The second probabilityin Equation (7) can be replaced by an additive branch metric (ABM)m_(a), where m_(a) is given in Equation (8) in which γ₁ and γ₂ areartificial constants. By properly setting γ₁ and γ₂, convenientexpressions for the ABM can be obtained. For example, if the symbol setis a uniform distribution, P(S_(k+1)|S_(k)) remains constant for allbranches where P is the a posteriori probability (APP). If we let γ₂=2σ²and the relation between γ₁ and γ₂ be as in Equation (9) then the ABMm_(a) (S_(k), S_(k+1)) is defined by Equation (10) where (ξ_(k)) is thenoiseless output (reference) of branch ξ_(k) and d is the Euclideandistance as defined earlier.

[0041] If the initial state S₁ is known, the expression in Equation (11)is true for any path ξ_(k) in the trellis diagram.

[0042] Define an additive accumulative path metric (APM) of path ξ_(k)aema (ξ_(k)) as the sum of the related ABM's, ie. as in Equation (12).

[0043] Therefore, the APM is a measure of the likelihood that the pathhas been actually transmitted, and the probability p (ξ_(k), z₁ ^(k))that the received samples between t=1 and k were transmitted via a pathξ_(k) is given in Equation (13).

[0044] For any arbitrary decision delay δ(L≦δ≧D), we can divide thepaths at time k into m mutually exclusive subsets Λ_(k) as given inEquation (14).

[0045] Obviously, the actually transmitted path belongs to one of thesubsets. The soft output algorithm (SSA) is suboptimal because it onlyconsiders the path with the minimum APM for each subset. The APM's ofthe m selected paths are adopted as the soft-output decision for signalU_(k-D). Therefore, we have the information packet illustrated inEquation (15).

[0046] The results are suboptimum in the sense that the selection of theinformation packet is a hardquantization process and the symbol errorprobability is not minimised. However, when a sequence of informationpacket is hard-quantized, the sequence error is minimised. Therefore, atmoderate-to-high SNR, the performance is quite acceptable.

Decision Feedback

[0047] The idea of decision feedback is that the trellis equaliser usesas much as possible the most prominent channel taps of the impulseresponse to form a reduced-states trellis structure for sequentialsymbol detection. The ISI caused by the rest of the taps of the impulseresponse are treated as an interference and deducted by the knowledge ofthe earlier estimated symbol information. For example, if we have thechannel impulse response h with memory length L=L1+L2. It is dividedinto two parts as given by Equation (16).

[0048] The first part of the channel impulse response (h_(O), . . .h_(L1)) is organised for an estimator to provide estimated channel tapsh_(O), . . . h_(L1) for setting up the trellis states in the trellisstructure while the second part (h_(L1), . . . h_(L1+L2)) is used forthe decision feedback as shown in the diagram in FIG. 3. In FIG. 3, asin FIG. 2, the blocks denoted Z⁻¹ represent path delays for individualtransmission paths. Reference numeral 4 denotes a summing function forsumming together all the channel taps h_(L) . . . h_(L). Referencenumeral 6 denotes a summing function for summing together only thechannel taps h_(L+1) . . . h_(L) which are to be treated asinterference. Reference numeral 8 denotes the subtraction function whichremoves as “interference” the part of the fed back sample correspondingto the channel taps h_(L1+1) . . . h_(L). Reference numeral 10 denotesthe summing and correlating function which generates from the fed backsignal samples and the estimated channel taps h_(L1+1) . . . h_(L1) thesignal “interference” which is to be removed from the incoming signalsamples z_(k). At time k, the received signal z_(k) is fed into thetrellis sequential estimation having first removed the interferencecaused by the second part of the impulse response as indicated inEquation (17) where (h_(L1+1), . . . h_(L1+L2)) are the estimated tapsof the second part of the channel response and (u_(k−(L1+1)), . . .u_(k−(L1+L2))) is the soft-output decision of the trellis equaliserhaving states defined by the first part of the estimated channel impulseresponse (h_(O), . . . h_(L1)).

[0049] As the performance of such an equaliser is much determined by theshape of the channel impulse response, it is desirable to use a minimumphase filter before the equaliser.

[0050] On the other hand, the decision value associated with each symbolalso affects the performance. According to the present system, asuitable softoutput decision has been developed which combines some kindof likelihood associated with each symbol that is actually transmitted.The likelihoods are combined together to form a soft output and are thenused for the decision feedback.

[0051] In the information packet from the soft-output algorithm (SSA)(Equation 15) the likelihood for the values of each symbol are linearlycombined together to give the soft output u_(k) in Equation (18) whereP_(k,m) is the minimum accumulative metric (APM) results from SSA andX_(m) is the combination coefficient.

[0052] To simplify the process, an Euclidean distance is defined betweenthe assumed signal value u_(k) (the reference) and the symbol A_(m)actually transmitted as in Equation (19).

[0053] As an approximation, Equation (19) can be used for the APM outputto derive the combination coefficient X_(m).

[0054] This gives rise to Equation (20).

[0055] With a sequential transmission u={A₁, A₂, A₃, . . . A_(M)}, it isnot difficult to derive the vector [X] from the matrix Equation (21).

[0056] For example, in a binary system (+1, −1), Equation (22) results.

EXPERIMENTAL RESULTS

[0057] A COSSAP block (DFSSA1) for the Sub-optimum Soft-output Algorithm(SSA) with both soft and hard delayed decision feedback has beenimplemented. The program is coded in C and has been tested together witha COSSAP test bed. The channel delay profile used is Outdoor-to-Indoor B[7] having 3.7 μs of delay spread.

[0058] A COSSAP block is a computer aided engineering environment fordesigning, simulating and implementing digital signal processing andcommunication systems.

[0059] Outdoor-to-Indoor B [7] is a defined channel model for a mobilecommunicaiton system (designed by FRAMES).

[0060]FIG. 4 shows the results from the simulations without theminimum-phase prefilter before the data entering the equaliser. Thechannel length is 6-symbol period with 7 taps, in which 4 taps (L₁=3)are used for the trellis definition and the rest of 3 taps (L₂=3) aretruncated which are used/or not used for the decision feedback. We cansee that the improvement with the decision feedback represented by HDF( - - - ) and SDF ( - - - ) is evident compared with the one withoutdecision feedback represented by NODF ( - - - - - - ). It is also to benoted that in the low SNR area (<10 dB), the result with soft decisionfeedback (SDF) gives about 0.1-0.3 dB gain over the one with harddecision feedback (HDF).

[0061]FIG. 5 shows the results from the simulations with theminimum-phase prefilter before the data entering the equaliser. Thechannel shape is much improved by the filter and the effect oftruncating the channel is less than those without the minimum-phaseprefilter. Anyway, the decision feedback gives better result than bysimply cutting the channel tail off.

[0062]FIG. 6 shows the comparison between the results from a full statesequaliser states (7 taps, number of states=2⁶=64) and a reduced-statesequaliser (4 taps, number of states=2³=8) with the decision feedback (3taps) . It seems that the decision feedback is a good trade-off betweenthe computational load and the system performance.

[0063] Having described a particular working embodiment, let a generalsituation be considered. A transmitted symbol can be expressed by thevector A and its likelihood output by vector A′ in the signal space. Ifan ellipse O is the noise region, the likelihood output can appearanywhere inside O due to the signal distortion by the noise +interference.

[0064] Define the uncertainty measure τ of the likelihood output:

τ=μ||A−A′||

[0065] where ||A−A′|| is the distance between A and A′, μ is a linearcoefficient for the uncertainty. The meaning of the uncertainty is thatif τ is small, the likelihood A′ is close to the transmitted symbol Aand the reliability is high. If τ is big, the noise level is high andsubsequent processes should rely less on the signal. The value of τshould be controlled within 0−1. If the noise is very strong and thelikelihood is run out of the ellipse O μ should be modified or τ shouldbe truncated to 1. Otherwise, the signal would be reverted.

[0066] A soft output S_(A) which contains the uncertainty measure forthe transmitted symbol A is given in Equation (23).

S _(A) =A(1−τ)=A(1−μ||A−A′||)  (23)

[0067] For a 1 D signal, if the transmitted data set is given byEquation 24.

Aε{a₁, a₂, a₃, . . . , a_(M)}  (24)

[0068] The soft output is given by Equation (25). $\begin{matrix}{S_{A} = {{\sum\limits_{i = 1}^{M}{a_{i} \cdot \left( {1 - \tau_{1}} \right)}} = {\sum\limits_{l = 1}^{M}{a_{i}\left( {1 - {\mu \cdot {{a_{i} - a_{i}^{\prime}}}}} \right)}}}} & (25)\end{matrix}$

[0069] where a_(i)′ is the likelihood of a_(i).

[0070] A by-product of this kind of soft decision method is that theuncertainty measure τ directly reflects the noise+interference level ofthe signal if let μ is 1. It can be used elsewhere in the receiver. Theexpectation of τ (E{τ}) is the variance of noise+interference. Forexample, the power control loop can be based on τ or E(τ).

[0071] In the above embodiment, the trellis equalizer can be arranged togive two likelihoods for the transmitted binary signal (+1/−1) and theyare in the form of the so-called accumulative survivor as in Equation(26).

[0072] $\begin{matrix}\begin{matrix}{{{ACC}\quad \_ \quad S_{= 1}} = {E\left\{ {{lk}_{= 1} + a_{{path} + {1{sum}}} + n_{= 1}} \right\}^{2}}} \\{= {{lk}_{= 1}^{2} + {E\left\{ {a_{{path} + {1{sum}}} + n_{+ 1}} \right\}^{2}}}} \\{{{ACC}\quad \_ \quad S_{- 1}} = {E\left\{ {{lk}_{- 1} + a_{{path} - {1{sum}}} + n_{- 1}} \right\}^{2}}} \\{= {{lk}_{- 1}^{2} + {E\left\{ {a_{{path} - {1{sum}}} + n_{- 1}} \right\}^{2}}}}\end{matrix} & (26)\end{matrix}$

[0073] If the signal and the noise are zero mean, we can take theaccumulative items (E{a_(path+1sum)+n₊₁}² and E{a_(path−1sum)+n_(−1}) ²)away from the likelihoods. Also we need an approximation as in Equation(27).

[0074] $\begin{matrix}\begin{matrix}{\Omega = {{{{ACC}\quad \_ \quad S_{+ 1}} - {{ACC}\quad \_ \quad S_{- 1}}}}^{1/2}} \\{= {{{lk}_{+ 1}^{2} - {lk}_{- 1}^{2}}}^{1/2}} \\{= {{{lk}_{+ 1} - {lk}_{- 1}}}}\end{matrix} & (27)\end{matrix}$

[0075] The final soft output for the decision feedback is then given byEquation (28).

S _(A)=sign(ACC _(—) S ⁻¹ −ACC _(—) S ₊₁)η(1−|1−Ω|)  (28)

[0076] $\begin{matrix}{{\text{~~~~}h} = \left\{ {h_{0},h_{1},{h2},\ldots \quad,h_{L - 1},h_{L}} \right\}} & (1) \\{{\text{~~~~}{\rho \left( n_{k} \right)}} = {\frac{1}{2\pi \quad \sigma^{2}}{\exp \quad\left\lbrack {- \frac{{n_{k}}^{2}}{2\quad \sigma^{2}}} \right\rbrack}}} & (2) \\{{{\text{~~~~}a_{k}} \in A}\overset{d < t}{=}\left\{ {A_{1},A_{2},\ldots \quad,A_{M}} \right\}} & (3) \\{{\text{~~~~}S_{k}}\overset{{d < t}\quad}{=}\left( {u_{k - L},\ldots \quad,u_{k - 2},u_{k - 1}} \right)} & (4) \\{{\text{~~~~}{d\left( \xi_{k} \right)}} = {{z_{k} - {\left( \xi_{k} \right)}}}} & (5) \\\begin{matrix}{{\text{~~~~}{p\left( {u_{k - D},z_{1}^{k}} \right)}} = {\sum\limits_{\forall S_{i - 1}}{p\left( {u_{k - D},S_{k + 1},z_{1}^{k}} \right)}}} \\{= {\sum\limits_{\forall S_{k - 1}}{{P\left( {\left. u_{k - D} \middle| S_{k + 1} \right.,z_{1}^{k}} \right)}{p\left( {S_{k + 1},z_{1}^{k}} \right)}}}}\end{matrix} & (6) \\\begin{matrix}{{\text{~~~~}{p\left( {S_{k + 1},z_{1}^{k}} \right)}} = {\sum\limits_{S_{t} \in Q}{p\left( {S_{k},S_{k + 1},z_{1}^{k}} \right)}}} \\{= {\sum\limits_{\forall S_{k - 1}}{{p\left( {S_{k},z_{1}^{k - 1}} \right)}{p\left( {S_{k + 1},\left. z_{l} \middle| S_{k} \right.,z_{1}^{k - 1}} \right)}}}}\end{matrix} & (7) \\{{\text{~~~~}{m_{a}\left( {S_{k},S_{k + 1}} \right)}}\overset{d + t}{=}{\gamma_{1} - {\gamma_{2}\ln \quad \left( {p\left( {S_{k + 1},\left. z_{k} \middle| S_{k} \right.} \right)} \right)}}} & (8) \\{{\text{~~~~}\gamma_{1}} = {\gamma_{2}\ln \quad \left( {\frac{1}{2{\pi\sigma}^{2}}{P\left( S_{k + 1} \middle| S_{\lambda} \right)}} \right)}} & (9) \\\begin{matrix}{{\text{~~~~}{m_{a}\left( {S_{k},S_{k + 1}} \right)}} = {d^{2}\left( {S_{k},S_{k + 1}} \right)}} \\{= {{z_{k} - {\left( \xi_{k} \right)}}}^{2}}\end{matrix} & (10) \\\begin{matrix}{{\text{~~~~}{p\left( {\zeta_{k}\quad,z_{1}^{k}} \right)}} = {p\left( {\zeta_{k},\left. z_{1}^{k} \middle| S_{1} \right.} \right)}} \\{= {{p\left( {S_{2},\left. z_{1} \middle| S_{1} \right.} \right)}{p\left( {S_{3},\left. z_{2} \middle| S_{2} \right.} \right)}\ldots \quad {p\left( {S_{k + 1},\left. z_{k} \middle| S_{k} \right.} \right)}}}\end{matrix} & (11) \\\begin{matrix}{{\text{~~~~}{{acm}_{a}\left( \zeta_{k} \right)}}\overset{d + t}{=}\quad {\sum\limits_{i = 1}^{k}{m_{a}\left( \xi_{k} \right)}}} \\{= \quad {{k\quad \gamma_{1}} - {\gamma_{2}{\ln \left( {p\left( {\zeta_{k},z_{1}^{k}} \right)} \right)}}}}\end{matrix} & (12) \\\begin{matrix}{{\text{~~~~}{p\left( {\zeta_{k},z_{1}^{k}} \right)}} \propto \quad {\exp \quad \left( {- \frac{m_{a}\left( \zeta_{k} \right)}{\gamma_{2}}} \right)}} \\{= \quad {\exp \quad \left( {- \frac{m_{a}\left( \zeta_{k} \right)}{2\sigma^{2}}} \right)}}\end{matrix} & (13) \\{{\text{~~~~}{\Lambda_{k}\left( {\delta,j} \right)}}\overset{\quad {d + t}}{=}{\left\{ {\left. \zeta_{k} \middle| u_{k - \delta} \right. = A_{j}} \right\} \quad \left( {{j = 1},2,\ldots \quad,M} \right)}} & (14) \\{{\text{~~~~}\left\{ \rho_{{k - D},j} \right\}} = {\left\{ {\min\limits_{\zeta_{k} \in {\Lambda_{t}{({D,j})}}}\left( {m_{a}\left( \zeta_{k} \right)} \right)} \right\} \quad \left( {{j = 1},2,\ldots \quad,M} \right)}} & (15) \\{{\text{~~~~}h} = \left\{ {h_{0},h_{1},{h2},\ldots \quad,h_{L1},h_{{L1} + 1},\ldots \quad,h_{{L1} + {L2}}} \right\}} & (16) \\{{\text{~~~~}z_{L}} = {z_{L} - {\sum\limits_{j = {{L1} + 1}}^{L_{1} + {L2}}{{\overset{\_}{u}}_{k - j}{\overset{\_}{h}}_{j}}}}} & (17) \\{{\text{~~~~}{\overset{\_}{u}}_{k}} = {\sum\limits_{m = 1}^{M}{\chi_{m}\rho_{k,m}}}} & (18) \\{{\text{~~~~}d_{k,m}} = {{u_{k} - A_{m}}}} & (19) \\{{\text{~~~~}{\overset{\_}{u}}_{k}} = {\sum\limits_{m = 1}^{M}{\chi_{m}d_{k,m}}}} & (20) \\{\begin{pmatrix}\chi_{1} \\\chi_{2} \\\chi_{3} \\\vdots \\\chi_{M}\end{pmatrix} = {\begin{pmatrix}0 & {{A_{1} - A_{2}}} & {{A_{1} - A_{3}}} & \cdots & {{A_{1} - A_{M}}} \\{{A_{2} - A_{1}}} & 0 & {{A_{2} - A_{3}}} & ⋰ & {{A_{2} - A_{M}}} \\{{A_{3} - A_{1}}} & {{A_{3} - A_{2}}} & 0 & ⋰ & {{A_{3} - A_{M}}} \\\vdots & ⋰ & ⋰ & ⋰ & \vdots \\{{A_{M} - A_{1}}} & {{A_{M} - A_{2}}} & {{A_{M} - A_{3}}} & \cdots & 0\end{pmatrix}^{- 1} \cdot \begin{pmatrix}A_{1} \\A_{2} \\A_{3} \\\vdots \\A_{M}\end{pmatrix}}} & (21) \\{{\text{~~~~}\begin{pmatrix}\chi_{1} \\\chi_{2}\end{pmatrix}} = \begin{pmatrix}{- 0.5} \\0.5\end{pmatrix}} & (22)\end{matrix}$

What is claimed is:
 1. A method of estimating symbols transmittedbetween a mobile station and a base station in a communication systemcomprising: receiving via a communication channel a set of receivedsignal samples (z_(k)) which have travelled via different transmissionpaths, each signal sample conveying a symbol component (A); estimatingfrom the set of received signal samples a soft-output decision for thesymbol (a) which combines over a number (M) of symbol components (A) anestimated value for each symbol component with a likelihood parameterwhich indicates a level of reliability associated with that estimatedvalue; and using the soft-output decision as a feedback element tomodify a subsequent set of received signal samples prior to estimating asoft output decision for the subsequent set of received samples.
 2. Amethod according to claim 1 , wherein a sequence of signal bursts arereceived via the communication channel and wherein a soft-outputdecision for each symbol in the signal burst is estimated and used as afeedback element prior to estimation of a subsequent symbol in the samesignal burst.
 3. A method according to claim 1 or 2 , wherein the stepof estimating a soft-output decision for the symbol (a) is carried outin a trellis equaliser in which state transitions are effected via a setof transition branches.
 4. A method according to claim 3 , wherein thestates for the trellis equaliser are initially defined by channel tapsof a channel impulse response estimated from the received signalsamples.
 5. A method according to claim 4 , wherein the channel impulseresponse comprises a number (L) of channel taps, wherein a first set ofthe channel taps (h₀ . . . h₁₁) is utilised for setting the initialstates in the trellis equaliser and a second set of the channel taps(h₁₁ . . . h₁) are treated as interference and used to modify the inputsignal prior to estimating a subsequent soft-output decision.
 6. Amethod according to claim 4 or 5 , wherein a minimum phase channelimpulse response is generated using an all path prefilter.
 7. A symbolestimation circuit for use in a mobile communication system forestimating symbols, the circuit comprising: a receiver arranged toreceive via a communication channel a set of signal samples (z_(k))which have travelled via different transmission paths, each signalsample conveying a symbol component; a estimator for estimating from theset of received signal samples a soft-output decision for the symbol (a)which combines over a number (M) of symbol components (A) an estimatedvalue for each symbol component with a likelihood parameter whichindicates a level of reliability associated with that estimated value;and a feedback path for feeding back the soft-output decision to modifya subsequent set of received signal samples prior to estimating asoftoutput decision for the subsequent set of received samples.
 8. Asymbol estimation circuit according to claim 7 , wherein the estimatortakes the form of a trellis equaliser.
 9. A symbol estimation circuit incombination with a channel estimator which generates a channel impulseresponse in the form of a set of channel taps, said channel taps beingused to define states in the trellis equaliser.
 10. A symbol estimationcircuit according to claim 9 , which comprises a memory for holding thechannel taps in two parts, a first part (h₀ . . . h₁₁) being used todefine said states in the trellis equaliser, and a second part beingused to modify the fed back soft-output decision.
 11. A symbolestimation circuit in combination with a channel estimator as claimed inclaim 10 , further comprising an all path filter for generating aminimum phase channel impulse response.